At the donut shop, 1/2 of their donuts have frosting. Of the donuts with frosting, 3/4 of them have sprinkles. How many donuts have both frosting and sprinkles?

Question

the answer is fraction!

Answer 1

To determine the fraction of donuts that have both frosting and sprinkles, we can start from the beginning.

Let’s assume the total number of donuts at the shop is \( D \).

1. Donuts with Frosting:
   According to the problem, \( \frac{1}{2} \) of the donuts have frosting. So, the number of donuts with frosting is:
   \[ \frac{1}{2} D \]

2. Donuts with Sprinkles:
   Of the donuts that have frosting, \( \frac{3}{4} \) have sprinkles. Therefore, the number of donuts that have both frosting and sprinkles is:
   \[ \frac{3}{4} \times \text{(donuts with frosting)} = \frac{3}{4} \times \frac{1}{2} D \]

3. Calculating the Fraction:
   Now calculate \( \frac{3}{4} \times \frac{1}{2} D \): \[ \frac{3}{4} \times \frac{1}{2} D = \frac{3 \times 1}{4 \times 2} D = \frac{3}{8} D \]

Thus, the fraction of the total donuts that have both frosting and sprinkles is \( \frac{3}{8} \).

Therefore, the final answer is: \[ \frac{3}{8} \]